F I NOLTR 69-106 VELOCITY PROFILE, SKIN-FRICTION BALANCE AND HEAT-TRANSFER MEASUREMENTS OF THE TURBULENT BOUNDARY LAYER AT MACH 5 AND ZERO-PRESSURE GRADIENT By R. E. Lee W. J. Yanta A. C. Leonas L 16 JUNE1969 DEC L! U UNITED STATES NAVAL ORDNANCE LABORATORY, WHITE OAK, MARYLAND II "1 V I,, 0% ce ,ATTENTION o This document has been approved for S public release and sale, its distribution is unlimited. '.
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FI
NOLTR 69-106
VELOCITY PROFILE, SKIN-FRICTION BALANCEAND HEAT-TRANSFER MEASUREMENTS OF THETURBULENT BOUNDARY LAYER AT MACH 5 ANDZERO-PRESSURE GRADIENT
ByR. E. LeeW. J. YantaA. C. Leonas
L 1 6 JUNE1969 DEC
L! U
UNITED STATES NAVAL ORDNANCE LABORATORY, WHITE OAK, MARYLANDII
"1 V I,,0%
ce ,ATTENTION
o This document has been approved forS public release and sale, its distribution
is unlimited.
'.
NOLTR 69-106
VELOCITY PROFILE, SKIN-FRICTION BALANCE AND HEAT-TRANSFERMEASUREMENTS OF THE TURBULENT BOUNDARY LAYER
AT MACH 5 AND ZERO-PRESSURE GRADIENT
Prepared by:R. E. Lee
W. J. YantaL A. C. Leonas
i ABSTRACT: The results of a detailed experimental investigationof a two-dimensional turbulent boundary layer at zero-pressuregradient are presented. The studi- were made at the free-stream
Mach number of 5, momentum-thickness Reynolds number from 4800to 56,000 and wall-to-adiabatic-wall temperature ratios from0.5 to 1.0. The data are in analytical terms of velocity profile,temperature profile, law-of-the-wall, velocity-defect law andincompressible form factor. Comparisons of local skin-frictioncoefficients obtained by four different experimental methods areshown. An empirical equation was derived from the shear-balancedata to calculate the friction coefficient from known values ofMach number, heat transfer and Reynolds number.
IiI
U. S. NAVAL ORDNANCE LABORATORYWHITE OAK, MARYLAND
II
NOLTR 69-106 16 June 1969
Velocity Profile, Skin-Friction Balance and Heat-TransferMeasurements of the Turbulent Boundary Layer at Mach 5 andZero-Pressure Gradient
This report presents the results of an extensive investigation ofa two-dimensional turbulent boundary layer at Mach 5 with moderateheat transfer in the NOL Boundary Layer Channel. The work wasperformed under the sponsorship of the Naval Air Systems Command,Task No. A32 320 148/292 I/R009-02-04.
The authors wish to acknowledge the support and assistance of theAerophysics Division of the U. S. Naval Ordnance Laboratory andin particular, wish to thank Mrs. C. D. Piper and Mr. D. L. Brottfor their assistance in obtaining an. reducing the data; andMessrs. F. W. Brown and F. C. Kemerer for the efficient operationof the facility and preparation of instrumentation.
3 Sunimary of Friction-Balance Data and Comparisonwith Empirical Relations
ILLUSTRATIONS
Figure
1 NOL Boundary Layer Channel Flexible Nozzle2 Operating Envelope for the NOL foundary Layer Channel,
Mach 5
3 Reynolds Number per Foot Capability, Mach 5
4 Schematic Showing Overall Layout of the Skin-FrictionBalance
a. Velocity Profiles at the 48-inch Stationb. Velocity Profiles at the 60-inch Stationc. Velocity Profiles at the 72-inch Stationd. Velocity Profiles at the 94-inch Station
Variation of Velocity Profile Exponent with Momentum-Thickness Reynolds Numbera. Static Temperature-Velocity Distribution at the48-inch Station
b. Static Temperature-Velocity Distribution at the60-inch Station
c. Static Temperature-Velocity Distribution at the72-inch Stationd. Static Temperature-Velocity Distribution at thei1-inch Station
8 a. Total Temperature Velocity Distribution, 48-inchStation, Tw/Taw = .73
b. Total Temperature Velocity Cistribution, 60-inchStation, Tw/Taw = .73
c. Total Temperature Velocity Distribution, 60-inchStation, po = 5 atms
d. Total Temperature Velocity Distribution, 72-inchStation, Tw/Taw = .73
e. Total Temperature Velocity Distribution, 72-inchStation, po = 5 atms
f. Total Temperature Velocity Distribution, 94-inchStation, Tw/Taw = .73
9 Correlation of Experimental Results in Terms of Law-of-the-Wall
iv
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II
{NOLTR 69-106~Figure
10 Correlation of Experimental Results in Terms ofVelocity Defect Law
11 Variation of Incompressible Form Factor with Momentum-Thickness Reynolds Number
12 a. Skin-Friction Correlation, 48-inch Stationb. Skin-Friction Correlation, 60-inch Stationc. Skin-Friction Correlation, 72-inch Stationd. Skin-Friction Correlation, 94-inch Station
13 Reynolds Analogy Factor as a Function of Momentum-Thickness Reynolds Number
14 Experimental Reynolds Analogy Correlation
15 Comparison of Friction-Balance Measurements,Tw/Taw = .73
16 Illustration of Probable Temperature Distribution ofVelocity Profile
17 Linear Portion of Velocity Prcfile fox Three Values ofTIV/Taw as Computed by the Method of Tetervin for M = 10
18 Effect of Wall Temperature on Local Friction CoefficientRe 20,000, M = 4.7
)
NOLTR 69-106
LIST OF SYMBOLS
Cf = local skin-friction coefficient based on balance dataB
C = local skin-friction coefficient based on heat-transfer data
c f = local skin-friction coefficient
D = defined in Fig. f0
H.n = incompressible form factor 6 /6i
M = Mach number, n = velocity power--profile exponent
Po = tunnel supply pressure
q = heat-transfer rate
ReI = momentum-thickness Reynolds number
St = Stanton number
T = temperature
T = as defined in Fig. 8
T = adiabatic wall temperatureaw
To 0 = tunnel supply temperature
Tt = local stagnation temperature
T t = local stagnation temperature at outer edge of boundary
layer
T = wall temperaturew
T = temperature at outer edge of boundary layer
u = velocity component in the x direction
u 6 = velocity at the outer edge of boundary layer
u* = shear velocity from shear-balance data 1"b/"w+ nondimensional velocity - u
x = nominal axial distance in flow direction measured from
The empirical nature ol compressible turbulent boundary-layertheories necessitates high-quality experimental data upon whichto base their formulations. Experimental studies of the boundarylayer in recent years generally employ techniques such as probingwith pressure and temperature probes to define the velocity anddensity profiles irom which the local skin friction can be inferred;direct measurement of the local shear force on a floating element;and various transient and steady-state heat-transfer techniquesto measure the heat transfer to the surface. The accuracy inprofile measurements is limited by the smallness of the boundary-layer tiickness and the relatively large probe sizes. The inference
of wall friction from the velocity gradient at the wall can veryeasily be swayed by errors due to the effect of probe-wallinterference. Floating element balances, which have been usedvery successfully in adiabatic-wall flows, are not as widely used
in flows with high heat transfers. In flows with heat -ransfer,usually profile or heat-transfer measurements are used to computethe friction drag. In the application of the latter, Reynoldsanalogy is assumed.
The present paper presents the results of employing fourdifferent experimental techniques to obtain the friction coefficientin a compressible turbulent boundary layer with heat transfer.These are: skin-friction balance, measurements inferred fromvelocity and temperature gradients, and local heat-transfermeasurements. Correlation of the profile and friction-coefficient
data with recent empirical methods are presented.
In addition, the results of detailed measurements of thevelocity and temperature profiles are presented. Analysis of thedata in terms of velocity-power profile, law-of-the-wall, velocity-defect law and incompressible form factor are given.
EXPERIMENTAL PROCEDURE AND INSTRUMENTATION
The experiments were conducted in the U. S. Naval OrdnanceLaboratory's Boundary Layer Channel at tunnel supply pressuresbetween 1 dnd 10 atmospheres and supply temperatures between 580ORand 12100 R. The momentum-thickness Reynolds number varied from4800 to 56,000 and wall to adiabatic-wall temperature ratio from0.5 to 1.0. These temperature ratios were attained by varying thesupply temperature and maintaining the wall temperature relativelyconstant. The main component of the facility is the two-dimensional
"1 supersonic nozzle illustrated in Figure 1. One wall of the nozzleis a flat plate and the opposite wall is a flexible plate whichmay lie adjusted to give flow Mach numbers between 3 and 7 at thenozzle exit. For the present investigations the plate contour was
adjusted to prescribe a Mach 5 uniform flow over the flat platebeginning at 55 inches downstream from the nozzle throat. Theoperating envelope and the Reynolds number per foot capability at
the Mach 5 setting are shown in Figures 2 and 3, respectively.Further details on the Channel and its performance are given inReference (1).
The model used for boundary-layer investigations is thenozzle flat plate. The plate, made of stainless steel, andinternally water cooled, is 8 feet long and tapered from 12 incheswide at the nozzle throat to 13.5 inches at the exit. Instrumen-tation ports, 1.875 inches in diameter, are provided along thecenter of the plate about every 12 inches apart starting 24 inchesdownstream of the nozzle throat. For the present investigationthe ports located at 48, 60, 72 and 94 inches from the throat wereused. Initial nozzle-design calculations using the methods ofReferences (2), (3), and (4) and Stanton-probe measurementsindicate the boundary layer to be turbulent at these locations forthe operating range described. Typical boundary-layer thicknessesalong the plate range from 2 to 4 inches.
The boundary-layer profile surveys were made by traversingindependently a Pitot pressure probe and an equilibrium conicaltemperature probe across the boundary layer. Each probe wasaligned with the probe tip located 2.75 inches upstream of thecenter of the instrumentation port. Each traverse was made fromthe free stream toward the plate with maximum probe movement of3.75 inches. The speed of traverse varied during the run toinsure that the probe had reached equilibrium conditions.
The profile data are recorded automatically and continuouslyon NOL's PADRE which is described in Reference (5). This unitprovides seven channels with servo-systems and direct digitalconversion to permit simultaneous sensing and recording of thedata directly on IBM cards.
Pitot-pressure probes were made of 0.125-inch diameterstainless-steel tubing flattened at the tip to a rectangular
opening of 0.016 x 0.100 inch. The local Mach number was computedfrom the Rayleigh Pitot tube formula using the measured Pitotand wall-static pressures.
The basic design of the equilibrium conical temperature probeis described in Reference (6). Essentially the equilibriumtemperature of a sharp 10-degree platinum cone was measured by athermocouple mounted onto its 0.050-inch diameter base. The conewas supported at its base by a 0.050-inch diameter, 0.5-inch longaluminum oxide tube, which also served to insulate the cone fromthe probe support mechanism. The measured cone temperature together
? with the measured lccal Mach number and cone tables provided thenecessary information to calculate the local stagnation and statictemperatures. A cone recovery factor equal to the square root ofthe P-- dt 1 number was assumed, based on the cone equilibriumtemperature.
2
NOLTR 69-106
The local velocity distribution was computed frcv the measuredMach number and temperature distributions. In the region of uniformflow, the experimental free-stream edge of the boundary layer isselected as the location where the slope of the velocity gradient
ubecomes zero, d- = 0. In the 48-inch station where pressure d
gradient exists in the free stream, the edge is selected where - =constant.
The basic design of the NOL skin-friction balance is describedin Reference (7). A schematic diagram illustrating its majorcomponents is shown in Figure 4. The instrument measured directlythe shear drag on a circular surface floating element mounted flushwith the flat plate. The element has an area of 0.5-square-inch. Thebalance was water-cooled and was designed for measurements inflows with heat transfer and pressure gradient.
Heat-transfer measurements were made by measuring theequilibrium temperature distribution in a stainless-steel rod,insulated around its circumference, and mounted with the axisnormal to the plate surface. Four iron-constantan thermocoupleswere welded to the rod at 0.25-inch intervals, measured from theend face of the rod that was mounted flush with the flat plate.The local skin-friction coefficient was computed from the
temperature gradient at the surface and the Colburn form of Reynoldsanalogy. One-dimensional heat flow along the axis of the rodwas assumed.
At the low operating supply pressure range, the boundarylayer was sufficiently thick such that temperature probing in theboundary-layer sublayer provides an accurate measurement of thetemperature gradient. For these cases, the heat transfer wascomputed as the product of the temperature gradient at the surfaceand the thermal conductivity of air at the surface temperature.Reynolds analogy was again used to obtain the friction coefficient.
EXPERIMENTAL RESULTS
Free-stream Pitot-pressure distributions measured with afive-finger rake as reported in Reference (1), showed the flow tobe uniform within ±0.75 percent of the free-stream Mach number inthe region from the 55-inch station to the end of the flat plate.Static-pressure probe surveys across the boundary layer from0.5 to 4.0 inches above the plate were made at the 60-inch and94-inch stations. They showed the static-pressure variation tobe within ±2.3 percent of the mean value at that station.Consequently, the static pressure was assumed to be constant.
The profile measurements in terms of local Mach number,static temperature, velocity and density are listed in Table 1.Graphs of the velocity profiles are shown in Figure 5. Because of
r3
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ;4
NOLTR 69-106
the thicker boundary layer at the one atmosphere pressure conditions,S it was possible to probe deep into the sublayer region, into the
linear portion of the velocity profile. For comparison, Figure 5Cshows computed velocity profiles using the numerical solution ofReference (8) for three supply temperatures. The numerical resultsagree reasonably well with the profile data at the lower tempera-ture, To = 7750 R, condition but differ considerably at the twohigher temperature surveys.
The dashed lines in Figure 5 show the velocity gradient deducedfrom the friction balance data. The balance results are also ingood agreement with the profile results except at the highertemperature runs.
A portion of the outer region can be readily fitted with apower profile. The variation of the power-profile exponent withmomentum-thickness Reynolds number is shown in Figure 6. The datawas citted by the method of least squares by the expression shown.The dependence of n with Ree appears to be independent of heat
I transfer.
The static temperature-velocity profiles are shown inFigure 7. A second order polynominal,
T u- = a + b (-) + c (- ()
was computed using the following boundary conditions to calculatethe coefficients a, b, and c:
T d(-- (T -T d d(.R-)0 T6 Taw w pr 1/3 6y 0, 1 , T '- = 0TdyT- T 6 dy
6, T = i, U6 1 (2)
Equation 1 is plotted in Figure 7. The polynomial appeared tofit the adiabatic wall temperature data satisfactorily, (seeFigure 7C, To - 6000 R) but did not give a good fit for the othercases where Tw/Taw < 1. For comparison the relations of Walz,Reference (9), and Crocco, Reference (10), are plotted in Figure 7B.
A widely used method of correlating temperature profile data,as suggested by the Crocco energy relation, is in terms of totaltemperature and velocity, see Reference (9), (11), (12), and (13).This is presented in Figure 8 together with three lines representingthe Crocco equation for unit Prandtl number; the zero heat-transferquadratic equation by Walz:
4
NOLTR 69-106
(U 2U6 (3)
and the following expression by Danberg, Reference (11):
T= (a) + 2
U6
where
T -Taw w-Tt w6
In general the present results follow the quadratic relation,equation (3), and are consistent with the general conclusion ofReferences (12) and (13) that data on the nozzle wall follow thequadratic rather than the Crocco relation. However, as shown inFigure 8, the data at the lowest Reynolds number at each stationshow a transition from the quadratic to the Crocco within thesublayer region. This trend was verified by independent measure-ments with the hot-wire temperature probe, see Reference (14).It has been suggested that the upstream boundary-layer historyand heat transfer to the wall can produce deviation from the linearCrocco relation. The details of this deviation and manner of itsrecovery need further investigation to better the understandingof turbulent boundary-layer flow.
The data in Figure 8 are presented in two groupings; for aconstant heat-transfer rate where Tw/Taw = 0.73 and for a constanttunnel supply pressure of five atmospheres. Little effect isnoted at the outer region of the boundary layer due to Reynoldsnumber variation. A systematic shift from the quadratic to the
a linear relation is noted as heat transfer increases or as the ratioTw/Taw decreases.
Comparisons of the profile results with the Law of the Wall andVelocity Defect Law are shown in Figures 9 and 10, respecti-'ely.The shear velocity was computed from shear balance data. TheIsolid line in the outer turbulent zone of Figure 9 is that reported
i I by Baronti and Libby, Reference (15), for adiabatic wall flows.
u = 2.43 ln(7.5 y+, (5)
In the Velocity Defect Law correlation of Figure 10, the solidlines represent empirical fits by Clauser and Hama, respectively,of incompressible flow data as reported in Reference (16). Theequations for these lines are:
5
NOLTR 69-106
- 2.44 in Z + 2.5 for - < 0.15 (6)
u -*U- 9.6(' - Y) for Z > 0.15 (7)U*6 6
A
It appeared that the correlations of the data in both Lawof the Wall and Velocity Defect Law showed a stronger dependencyon heat transfer as expressed in Tw/Taw ratio rather than onReynolds number.
Correlation of the data in terms of the incompressible formfactor is shown in Figure 11. The present results and also theresults of Winkler-Cha, Reference (17), as shown are parallel tothe Tetervin-Lin fit of incompressible flow data, see Reference (18).The dotted line was drawn parallel to the Tetervin-Lin curve butdisplaced to go through the present data. The third line drawnwas obtained by use of power profiles and Figure 6.
where H. _ inc 2 + 1 (8)inc 0. ninc
The data did not show any trend due to heat transfer.
The skin-friction coefficient obtained by the four experimentalmethods at the four test stations are shown in Figure 12. For
comparison, predictions shown were those of Spalding-Chi.Reference (19); Falkner and Blasius, Reference (20); Persh,Reference (21); and Winkler-Cha, Reference (17). These predictedvalues represented by the lines were computed for Tw/Taw = .73where most of the experimental data were taken. Generally, theshear balance data are about 20 percent lower than the widelyaccepted prediction of Spalding-Chi. The velocity profile datashowed more scatter than the balance data, reflecting the difficultyof obtaining accurate friction coefficients from profile measure-ments.
Friction coefficients obtained from heat-transfer data as
shown in Figures 12B and 12C and tabulated in Table 2 indicate amarked deviation from those based on balance measurements withincreasing Reynolds number. This may be a consequence of assuminga constant turbulent flow recovery factor of 0.89 and the acceptanceof the Colburn form of Reynolds analogy.
2St_ Pr-2/ 3 (9)cf
6
___ _ __1j
iA
NOLTR 69-106
The present data show a Reynolds number effect on the Reynoldsanalogy factor which is stronger than indicated by Tetervin,Reference (22). This is shown in Figure 13. Figure 14 is acomparison of the present results with those of Danberg, Refer-ence (11) for similar heat-transfer range. It appears that furtherstudies are needed in this area to relate heat transfer to skinfriction.
The balance data from the four measuring stations for Tw/Taw -
.73 are replotted in Figure 15. Very good agreement was obtainedbetween the measurements at the 60, 72, and 94-inch stations.The measurements at the 48-inch station were higher than the othersbecause they were in the pressure drop region of the nozzle. Thegood agreement of the data at the three downstream stationsindicated that pressure gradient history at the upstream end of theplate was "forgotten" and the local flow was similar to zeropressure gradient flat plate flow. The data from the downstreamthree measuring stations were fitted by the least-square method toobtain tke following relation:
cf = 0.0211 Re0 - 0 "I 0 (11)
which fits the experimental data to 7.5 percent. In contrast, thesimilar balance data at the 48-inch station, which was in thepressure drop region, resulted in a parallel line with higherfriction coeffiuients.
Further analysis of the experimental data in Figure 12
indicated that at decreasing values of Tw/Taw, both the balanceand heat-transfer results showed cf to increase slightly whereasthe velocity-profile measurements showed the opposite trend.It can be speculated that the cooling of the wall car. introducecurvature of the velocity profile very near the wall as illustratedin Figure 16. Figure 16A represents a typical temperature distri-bution in the boundary layer with wall c:oling. If it is assumedthat the coefficient of viscosity is proportional to the tempera-ture and the shear is constant some distance past the peak of thetemperature curve then the velocity gradient most complement thetemperature distribution as shown in Figure 16B for the equationshown in the figure to be true. Integrating the curve of Figure 16Bwill result in the velocity distribution of Figure 16C where a humpwould exist near the wall. The interpretation of the data outsidethis hump would lead to the slope shown by the dotted line andresult in a lower value of the shear force. Unfortunately thesize of probes used in the present investigation made it difficultto distinguish between probe interference and temperaturedistortion of the boundary layer. Numerical calculations of theturbulent boundary layer by the method of Tetervin, Reference (8)add some support to this theory. The calculations were made for
I_7
NOLTR 69-106
Mach 10 flow with three assumed values of Tw/Taw and is shown inFigure 17. Although no hump appeared, the curved portion of thevelocity profile extends closer to the wall as Tw/Taw is decreasedand consequently the error in estimating the slope of the velocityprofile at the wall when obtained by a fairing of experimentalpoints not very near the wall becomes larger. Figure 17 indicatesthat the size limitation of present probing techniques rendersthis method of obtaining friction coefficients inaccurate for very Icold walls.
Further correlation of the wall temperature effect on frictioncoefficients as obtained by the velocity profile technique anddirect force measurement are shown in Figure 18 for one ,value ofReynolds number. The balance results showed a slight increase incf due to wall temperature and the friction coefficients were lowerthan predicted by the Spalding-Chi method. The velocity-profileresults reflected the above analysis and were in general agreementwith the results of Winkler-Cha which were based on profile measure-!ments at Tw/Taw greater than 0.61.
The present data was fitted by the method of least squares bythe equation shown in Figure 18. The basic form of the equationwas adapted from Reference (17) and the coefficient and exponentsfor- the heat transfer and Reynolds number terms adjusted to fit
the present data. The Mach number dependency term, (T0/T$), wascarried over from Reference (17). This equation describesthepresent data to within 6.6 percent as shown in Table 3.
CONCLUSION 1
The turbulent boundary layer in the NOL Boundary LayerChannel at Mach 5; 4800 < Rea < 56,000; .48 < Tw/Taw < 1.0; wasstudied with pressure and temperature probes, a shear balance,
and a heat-transfer gage.
The structure of the boundary layer was examined in terms ofvelocity and temperature profiles, law of the wall, velocity-defectlaw and incompressible forn factor. Data was obtained to y = 1.4;this is much closer to the wall than previously obtained. Theouter portion of the velocity profile can be fitted by a powerprofile. A relation between power-profile exponent and momentum-
thickness Reynolds number was derived. Correlation of theincompressible form factor showed similarity witn subsonic flowresults. An expression relating the form factor with momentum-thickness Reynolds number was given.
Local skin-friction coefficients obtained from shear-balancemeasurements, velocity-profile data, temperature-profile data andheat-transfer data were compared. The balance results were themost consistent of the four and were about 20 percent lower thanthe prediction of Spalding-Chi. Heat-transfer measurements showed
8
-~ ~ ~ * j -
<A
NOLTR 69-106
a marked disagreement with shear-balance measurements at highReynolds numbers. The Reynolds analogy factor is strongly affectedby Reynolds number. The local skin-friction coefficient asmeasured with shear ba]. zce and a heat-transfer gage increasedslightly as Tw/Taw decreased. Velocity-profile measurementsindicated the opposite trend. The distortion of the velocityprofile very close to the wall by heat transfer was a suggestedcause. This was supported by calculations by Tetervin's method.An equation was obtained by the least-square fit of the data tocompute the local friction coefficient. This equation accountsfor variatio-s in Mach number, heat transfer and Reynolds numberand represents the present data to within 6.6 percent.
The data showed some evidence of the upstream boundary-layerhistory and the heat transfer on boundary-layer profiles. Theresults indicate that both the friction drag and velocity profilewill quickly adjust to local flat-plate conditions while thetemperature profile will retain a memory of the upstream conditionsfor a long time. Additional analytical and experimental studiesare needed to verify these findings and to better the understandingof turbulent boundary-layer flow.
A 9
NOLTR 69-106
REFERENCES
1. Lee, R. E.,Yanta, W. J., Leonas, A. C. and Carner, J.,"The NOL Boundary Layer Channel," NOLTR 66-185, Nov 1966
2. Persh, J., "A Procecure for Calculating the Boundary LayerDevelopment in the Region of Transition from Laminar toTurbulent Flow," NAVORD Relort 4438, Mar 1957
3. Squires, K., Roberts, R., and Fisher, E., "A Method forDesigning Supersonic Nozzles Using the Centerline MachNumber Distribution," NAVORD Report 3995, Oct 1956
4. Persh, J. and Lee, R., "A Method for Calculating TurbulentBoundary Layer Development in Supersonic and HypersonicNozzles Including the Effects of Heat Transfer," NAVORDReport 4200, 7 Jun 1956
5. Kendall, J. M., "Portable Automatic Data Recording Equipment(PADRE)," NAVORD Report 4207, Aug 1959
6. Danberg, J. E., "The Equilibrium Temperature Probe, a Devicefor Measuring Temperatures in a Hypersonic Boundary Layer,"NOLTR 61-2, Dec 1961
7. Durgin, F. H., "The Design and Preliminary Testing of a DirectMeasuring Skin Friction Meter for Use in the Presence of HeatTransfer," MIT Aerophysics Laboratory Tech. Report 93, Jun 1964
8. Tetervin, N., "An Analytical Investigation of the Flat PlateTurbulent Boundary Layer in Compressible Flow," NOLTR 67-39,May 1967
9. Walz, A., "Compressible Turbulent Boundary Layers,"The Mechanics of Turbulence, New York, Science PublishersInc., 1964 (Proceedings of Colloque International sur"La M6chanique de la Turbulence," Marseille, Aug 28 to
11. Danberg, I. E., Winkler, E. M., Chang, P. K., "Heat andMass Transfer in a Hypersonic Turbulent Boundary Layer,"Proceedings of the 1965 Heat Transfer and Fluid MechanicsInstitute, Paper No. 8, Jun 1965
12. Bertram, M. H. and Neal, L., Jr., "Recent Experiments inHypersonic Turbulent Boundary Layers," NASA TMS-56335,1965
10
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NOLTR 69-106
13. Wellace, J. E., "Hypersonic Turbulent Boundary Layer Studiesat Cold Wall Conditions," Proceedings of the 1967 HeatTransfer and Fluid Mechanics Institute, Paper No. 22,Jun 1967, pp 427-451
14. Yanta, W. J., "A Hot-Wire Stagnation Temperature Probe,"NOLTR 68-60, Jun 1968
15 Barconti, P. 0. and Libby, P. A.,"Velocity Profiles inTurbulent Compiessible Boundary Layers," AIAA Journal,Vol. 4, No. 2, Fab 1966, p 193
16. Daily, J. W. and Hai~eman, D. R. F., "Fluid Dynamics,"Addison-Wesley Publishing Company, Inc., Mass., 1966, p 236
17. Winkler, E. M. ane Cha, M. H., "Investigation of Flat PlateHypersonic Turbulet Boundary Layers with Heat Transfer ata Mach Number of 5.2," NAVORD Report 6631, Sep 1959
18. Tetervin, N. and Lin, C. C., "A General Integral Form of theBoundary Layer Equation for Incompressible Flow with anApplication to the Calculation of the Separation Point ofTurbulent Boundary Layers," NACA Report 1046, 1951
19. Spalding, D. B. and Chi, S. W., "The Drag of a CompressibleTurbulent Boundary Layer on a Smooth Flat Plate With and
Without Heat Transfer," J. Fluid Mechanics, Vol. 18, Pt. 1,Jan 1964, pp 117-143
20. Thwaites, B., "Incompressible Aerodynamics," Oxford UniversityPress, 1960 T
21. Persh, J., "A Theoretical Investigation of Turbulent BoundaryLayer Flow with Heat Transfer at Supersonic and HypersonicSpeed," NAVORD 3854, 1954
22. Tetervin, N., "An Analytical Investigation of the Flat PlateTurbulent Boundary Layer in Compressible Flow," NOLTR 67-39,15 May 1967
11 j.
_ _.___I
NO LTR 69-106
032 TO 3 000
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NO LTR 69-106
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FIG. 3 REYNOLDS NUMBER PER FOOT CAPABILITY, MACH 5
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40 w 0 0 w 0 N 0 10 40 . 0 N ( - 4 . 0 . 4 1
o. a - N0 0. .44 N .44 N. m4 C44 N Nr N '4 .4 N.4 I 4 I I I I I I 4 I I
-- - - -- - - -- - - - -- - - -- - - -r, C -e
UNCLASSIFIEDSecurity Classification
DOCUMENT CONTROL DATA. R & D(Security classlication of title, body of abstract and indexing annotation must be entered when the overall report is clashifled)
1 ORIGINATING ACTIVITY (Corporate authOr) A. REPORT SECURITY CLASSIFICATION
I U. S. Naval Ordnance Laboratory JUNCLASSIFIEDWhite Oak, Silver Spring, Maryland 2b. GROUe
3. REPORT TITLE
Velocity Profile, Skin--FricLion Balance and Heat-Transfer Measurementsof the Turbulent Boundary Layer at Mach 5 and Zero-Pressure Gradient.
4. DESCRIPTIVE NOTES (Typo of report and Inclusive dates)
final5. AU THOR(S) (First name, middle initial, last naine)
Roland E. Lee, William J. Yanta and Annette C. Leonas
6. REPORT DATE 7a. TOTAL NO. OF PAGES [7b. 1,. OF REFS
16 June 1969 14 plus illus. 22le. CONTRACT OR GRANT NO. go. ORIGINATOR'S RCPORT NUMBER(S)
This document has been approved for public release and sale, itsdistribution is unlimited.
It. SUPPLEMENTARY NOTES 112. SPONSORING MILITARY ACTIVITY
13 ABSTRACT
" .The results of a detailed experimental investigation of atwo-dimensional turbulent boundary layer at zero-pressure gradient arepresented. The studies were made at the free-stream Mach number of 5,momentum-thickness Reynolds number from 4800 to 56,000 and wall-to-adiabatic-wall temperature ratios from 0.5 to 1.0. The data are inanalytical terms of velocity profile, temperature profile, law-of-the-wall, velocity-defect law and incompressible form factor. Comparisonsof local skin-friction coefficients obtained by four differentexperimental methods are shown. An empirical equation was derivedfrcm the shear-balance data to calculate the friction coefficient fromknown values of Mach number, heat transfer and Reynolds number. )
I'
DD ,OvS1473 ,U NCLASSIFIED
S/N 0101-807,6801 Security Classification
UNCLASSIFIEDsecurity Ciassification LN I -0LN
KEY WOROS ROE ;T ROLE WT ROLE WT
1. Boundary layer2. compressible3. Turbulent4. Profile5. Pressure gradient6. Velocity7. Skin friction8. Mach number9, Temperature ratio10. Reynolds number
t DDFORM 143(BACK) UNCLASSIFIEDSecurity ClassificatiOnI (PAGE 2)